dane:
R = 50 cm
x₁ = 80 cm
x₂ = x₁ + 20 cm = 100 cm
szukane:
|y₁ - y₂| = ?
f = R/2 = 25 cm
1/f = 1/x + 1/y
1/y = 1/f - 1/x
1/y = (x - f)/fx
y = fx/(x - f)
y₁ = fx₁/(x₁ - f)
y₂ = fx₂/(x₂ - f)
|y₁ - y₂| = |fx₁/(x₁ - f) - fx₂/(x₂ - f)| = f|x₁/(x₁ - f) - x₂/(x₂ - f)|
|y₁ - y₂| = 25 cm |80 cm/(80 cm - 25 cm) - 100 cm/(100 cm - 25 cm)| = 25 cm |80 cm/55 cm - 100 cm/75 cm| = 25 cm |16/11 - 4/3| = 25 cm |48/33 - 44/33| = 25 cm * 4/33 = 3 1/33 cm
